Geodesic
A difference scheme for a~conjugate-operator model of the heat conduction problem in the polar coordinates
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 3, pp. 297-312

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In the polar coordinates, a discrete analog of the conjugate-operator model of the heat conduction problem preserves the structure of the original model. The difference scheme converges with the second order of accuracy for the cases of discontinuous parameters of the medium in the Fourier law and irregular grids. An efficient algorithm for solving the discrete conjugate-operator model in the case when the thermal conductivity tensor is a single operator. 
@article{SJVM_2017_20_3_a5,
     author = {S. B. Sorokin},
     title = {A difference scheme for a~conjugate-operator model of the heat conduction problem in the polar coordinates},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {297--312},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a5/}
}
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S. B. Sorokin. A difference scheme for a~conjugate-operator model of the heat conduction problem in the polar coordinates. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 3, pp. 297-312. http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a5/